A battery manufacturer tests its newly developed EV battery by constructing a mean chart for controlling...

A battery manufacturer tests its newly developed EV battery by constructing a mean chart for controlling the service life of a fully charged battery. The company knows from previous samples that when the service life is in control it is normally distributed with a mean of 500 hours and a standard deviation of 10 hours. On three recent production batches, the firm tested service life on random samples of four batteries, with these results: Sample Service Life (hours) 1 495 500 505 500 2 525 515 505 515 3 494 485 506 499 What is the mean of the sampling distribution of sample means when the service life is in control? 500 What is the sample mean service life for sample 3? 496 What is the standard deviation of the sampling distribution of sample means for whenever service life is in control? 5 If he uses upper and lower control limits of 505 and 495 hours, what is his risk (alpha) of concluding that service life is out of control when it is actually under control (Type I error Normal table.pdf )? 1 (Provide your answer in 0.**** format) If he uses upper and lower control limits of 505 and 495 hours, on what sample(s) (if any) does service life appear to be out of control?

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